Precalculus (6th Edition)

Published by Pearson
ISBN 10: 013421742X
ISBN 13: 978-0-13421-742-0

Chapter 1 - Equations and Inequalities - 1.8 Absolute Value Equations and Inequalities - 1.8 Exercises - Page 167: 23


All values of $x$ are a solution of this equation.

Work Step by Step

$|5x-2|=|2-5x|$ Solving this absolute value equation is equivalent to solving two separate equations, which are: $5x-2=2-5x$ and $5x-2=-(2-5x)$ $\textbf{Solve the first equation:}$ $5x-2=2-5x$ Take $5x$ to the left side and $2$ to the right side: $5x+5x=2+2$ $10x=4$ Solve for $x$: $x=\dfrac{4}{10}$ $x=\dfrac{2}{5}$ $\textbf{Solve the second equation:}$ $5x-2=-(2-5x)$ $5x-2=5x-2$ $5x-5x=-2+2$ $0=0$ This equation is an identity. It is true for all values of $x$ All values of $x$ are a solution of this equation.
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